Bloch Tight-Binding Oscillations

Discover why a constant force can produce oscillation inside a periodic energy band rather than a continuous unbound acceleration.

Experiment

Using the Bloch Tight-Binding Oscillations module, adjust the 'Force' control to 1, and watch how the 'Displacement' and 'Momentum phase' variables evolve with the 'Time' control. This demonstrates real-space oscillations instead of unbound acceleration.

1. Set the initial state by keeping Hopping at 1, Force at 1, Time at 0, and Initial momentum at 0. Observe the zero displacement and ground state energy E = -2.
2. Gradually advance the Time control. Notice how the particle accelerates initially but its velocity maxes out and then begins to drop as it climbs the energy band.
3. At Time π, observe that the group velocity drops to 0, representing the classical turning point in real space despite a constant forward force.
4. Reset Force to 0 and observe the uniform non-oscillatory motion, showing how the lack of force leads to ballistic transport at constant velocity.